Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(89,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1277.6 | ||
Character | \(\chi\) | \(=\) | 1386.1277 |
Dual form | 1386.2.r.d.89.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −2.01268 | − | 3.48607i | −0.900098 | − | 1.55902i | −0.827365 | − | 0.561664i | \(-0.810161\pi\) |
−0.0727330 | − | 0.997351i | \(-0.523172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64157 | + | 0.148737i | 0.998419 | + | 0.0562173i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.48607 | + | 2.01268i | 1.10239 | + | 0.636466i | ||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.78421i | − | 1.60425i | −0.597156 | − | 0.802125i | \(-0.703703\pi\) | ||
0.597156 | − | 0.802125i | \(-0.296297\pi\) | |||||||
\(14\) | −2.36203 | + | 1.19197i | −0.631280 | + | 0.318568i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.655680 | − | 1.13567i | 0.159026 | − | 0.275440i | −0.775492 | − | 0.631357i | \(-0.782498\pi\) |
0.934518 | + | 0.355917i | \(0.115831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.95486 | − | 3.43804i | 1.36614 | − | 0.788741i | 0.375706 | − | 0.926739i | \(-0.377400\pi\) |
0.990432 | + | 0.137998i | \(0.0440668\pi\) | |||||||
\(20\) | −4.02536 | −0.900098 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −2.08402 | + | 1.20321i | −0.434548 | + | 0.250887i | −0.701282 | − | 0.712884i | \(-0.747389\pi\) |
0.266734 | + | 0.963770i | \(0.414055\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.60177 | + | 9.70255i | −1.12035 | + | 1.94051i | ||||
\(26\) | 2.89210 | + | 5.00927i | 0.567188 | + | 0.982399i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.44959 | − | 2.21330i | 0.273947 | − | 0.418274i | ||||
\(29\) | 0.530917i | 0.0985888i | 0.998784 | + | 0.0492944i | \(0.0156972\pi\) | ||||
−0.998784 | + | 0.0492944i | \(0.984303\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.04209 | − | 1.17900i | −0.366770 | − | 0.211755i | 0.305276 | − | 0.952264i | \(-0.401251\pi\) |
−0.672046 | + | 0.740509i | \(0.734585\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.31136i | 0.224896i | ||||||||
\(35\) | −4.79812 | − | 9.50804i | −0.811031 | − | 1.60715i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.33840 | + | 7.51433i | 0.713229 | + | 1.23535i | 0.963639 | + | 0.267209i | \(0.0861013\pi\) |
−0.250410 | + | 0.968140i | \(0.580565\pi\) | |||||||
\(38\) | −3.43804 | + | 5.95486i | −0.557724 | + | 0.966006i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.48607 | − | 2.01268i | 0.551195 | − | 0.318233i | ||||
\(41\) | 5.27341 | 0.823569 | 0.411784 | − | 0.911281i | \(-0.364906\pi\) | ||||
0.411784 | + | 0.911281i | \(0.364906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.642009 | 0.0979055 | 0.0489527 | − | 0.998801i | \(-0.484412\pi\) | ||||
0.0489527 | + | 0.998801i | \(0.484412\pi\) | |||||||
\(44\) | 0.866025 | − | 0.500000i | 0.130558 | − | 0.0753778i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.20321 | − | 2.08402i | 0.177404 | − | 0.307272i | ||||
\(47\) | −5.99941 | − | 10.3913i | −0.875104 | − | 1.51572i | −0.856652 | − | 0.515895i | \(-0.827459\pi\) |
−0.0184524 | − | 0.999830i | \(-0.505874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95575 | + | 0.785798i | 0.993679 | + | 0.112257i | ||||
\(50\) | − | 11.2035i | − | 1.58442i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.00927 | − | 2.89210i | −0.694661 | − | 0.401063i | ||||
\(53\) | −2.35898 | − | 1.36196i | −0.324031 | − | 0.187079i | 0.329157 | − | 0.944275i | \(-0.393235\pi\) |
−0.653188 | + | 0.757196i | \(0.726569\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.02536i | − | 0.542780i | ||||||
\(56\) | −0.148737 | + | 2.64157i | −0.0198758 | + | 0.352994i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.265458 | − | 0.459787i | −0.0348564 | − | 0.0603730i | ||||
\(59\) | 0.834008 | − | 1.44455i | 0.108579 | − | 0.188064i | −0.806616 | − | 0.591076i | \(-0.798703\pi\) |
0.915195 | + | 0.403012i | \(0.132037\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.2851 | + | 7.67018i | −1.70099 | + | 0.982066i | −0.756226 | + | 0.654310i | \(0.772959\pi\) |
−0.944762 | + | 0.327756i | \(0.893708\pi\) | |||||||
\(62\) | 2.35800 | 0.299467 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −20.1641 | + | 11.6418i | −2.50105 | + | 1.44398i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.09028 | + | 5.35251i | −0.377537 | + | 0.653914i | −0.990703 | − | 0.136040i | \(-0.956562\pi\) |
0.613166 | + | 0.789954i | \(0.289896\pi\) | |||||||
\(68\) | −0.655680 | − | 1.13567i | −0.0795128 | − | 0.137720i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.90932 | + | 5.83514i | 1.06487 | + | 0.697432i | ||||
\(71\) | − | 12.0531i | − | 1.43044i | −0.698901 | − | 0.715219i | \(-0.746327\pi\) | ||
0.698901 | − | 0.715219i | \(-0.253673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5428 | − | 6.08687i | −1.23394 | − | 0.712414i | −0.266089 | − | 0.963948i | \(-0.585732\pi\) |
−0.967848 | + | 0.251534i | \(0.919065\pi\) | |||||||
\(74\) | −7.51433 | − | 4.33840i | −0.873523 | − | 0.504329i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 6.87608i | − | 0.788741i | ||||||
\(77\) | 2.21330 | + | 1.44959i | 0.252228 | + | 0.165197i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.70820 | − | 9.88689i | −0.642222 | − | 1.11236i | −0.984936 | − | 0.172922i | \(-0.944679\pi\) |
0.342713 | − | 0.939440i | \(-0.388654\pi\) | |||||||
\(80\) | −2.01268 | + | 3.48607i | −0.225025 | + | 0.389754i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.56691 | + | 2.63671i | −0.504331 | + | 0.291176i | ||||
\(83\) | 13.1957 | 1.44841 | 0.724207 | − | 0.689582i | \(-0.242206\pi\) | ||||
0.724207 | + | 0.689582i | \(0.242206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.27869 | −0.572555 | ||||||||
\(86\) | −0.555996 | + | 0.321005i | −0.0599546 | + | 0.0346148i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −1.06857 | − | 1.85081i | −0.113268 | − | 0.196185i | 0.803818 | − | 0.594875i | \(-0.202798\pi\) |
−0.917086 | + | 0.398690i | \(0.869465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.860326 | − | 15.2794i | 0.0901867 | − | 1.60171i | ||||
\(92\) | 2.40642i | 0.250887i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3913 | + | 5.99941i | 1.07178 | + | 0.618792i | ||||
\(95\) | −23.9705 | − | 13.8394i | −2.45932 | − | 1.41989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.3836i | − | 1.56197i | −0.624552 | − | 0.780983i | \(-0.714719\pi\) | ||
0.624552 | − | 0.780983i | \(-0.285281\pi\) | |||||||
\(98\) | −6.41676 | + | 2.79736i | −0.648191 | + | 0.282576i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.60177 | + | 9.70255i | 0.560177 | + | 0.970255i | ||||
\(101\) | −8.06738 | + | 13.9731i | −0.802734 | + | 1.39038i | 0.115075 | + | 0.993357i | \(0.463289\pi\) |
−0.917810 | + | 0.397020i | \(0.870044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.26648 | + | 2.46325i | −0.420388 | + | 0.242711i | −0.695243 | − | 0.718774i | \(-0.744703\pi\) |
0.274855 | + | 0.961486i | \(0.411370\pi\) | |||||||
\(104\) | 5.78421 | 0.567188 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.72392 | 0.264570 | ||||||||
\(107\) | −5.46644 | + | 3.15605i | −0.528461 | + | 0.305107i | −0.740389 | − | 0.672178i | \(-0.765359\pi\) |
0.211929 | + | 0.977285i | \(0.432026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.23197 | − | 15.9902i | 0.884262 | − | 1.53159i | 0.0377057 | − | 0.999289i | \(-0.487995\pi\) |
0.846557 | − | 0.532299i | \(-0.178672\pi\) | |||||||
\(110\) | 2.01268 | + | 3.48607i | 0.191902 | + | 0.332383i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.19197 | − | 2.36203i | −0.112631 | − | 0.223191i | ||||
\(113\) | − | 2.47936i | − | 0.233239i | −0.993177 | − | 0.116619i | \(-0.962794\pi\) | ||
0.993177 | − | 0.116619i | \(-0.0372058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.38894 | + | 4.84335i | 0.782272 | + | 0.451645i | ||||
\(116\) | 0.459787 | + | 0.265458i | 0.0426902 | + | 0.0246472i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.66802i | 0.153553i | ||||||||
\(119\) | 1.90094 | − | 2.90243i | 0.174259 | − | 0.266065i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.500000 | + | 0.866025i | 0.0454545 | + | 0.0787296i | ||||
\(122\) | 7.67018 | − | 13.2851i | 0.694426 | − | 1.20278i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.04209 | + | 1.17900i | −0.183385 | + | 0.105877i | ||||
\(125\) | 24.9715 | 2.23352 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.20830 | −0.462161 | −0.231081 | − | 0.972935i | \(-0.574226\pi\) | ||||
−0.231081 | + | 0.972935i | \(0.574226\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.6418 | − | 20.1641i | 1.02105 | − | 1.76851i | ||||
\(131\) | 5.39304 | + | 9.34102i | 0.471192 | + | 0.816128i | 0.999457 | − | 0.0329512i | \(-0.0104906\pi\) |
−0.528265 | + | 0.849080i | \(0.677157\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 16.2415 | − | 8.19611i | 1.40832 | − | 0.710693i | ||||
\(134\) | − | 6.18055i | − | 0.533918i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.13567 | + | 0.655680i | 0.0973829 | + | 0.0562241i | ||||
\(137\) | 10.8079 | + | 6.23994i | 0.923380 | + | 0.533114i | 0.884712 | − | 0.466138i | \(-0.154355\pi\) |
0.0386683 | + | 0.999252i | \(0.487688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.51846i | 0.213613i | 0.994280 | + | 0.106806i | \(0.0340625\pi\) | ||||
−0.994280 | + | 0.106806i | \(0.965937\pi\) | |||||||
\(140\) | −10.6333 | − | 0.598720i | −0.898675 | − | 0.0506011i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.02654 | + | 10.4383i | 0.505736 | + | 0.875961i | ||||
\(143\) | 2.89210 | − | 5.00927i | 0.241850 | − | 0.418896i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.85081 | − | 1.06857i | 0.153701 | − | 0.0887396i | ||||
\(146\) | 12.1737 | 1.00751 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.67680 | 0.713229 | ||||||||
\(149\) | 8.50142 | − | 4.90830i | 0.696464 | − | 0.402103i | −0.109565 | − | 0.993980i | \(-0.534946\pi\) |
0.806029 | + | 0.591876i | \(0.201613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.77440 | + | 8.26951i | −0.388535 | + | 0.672963i | −0.992253 | − | 0.124235i | \(-0.960352\pi\) |
0.603717 | + | 0.797198i | \(0.293686\pi\) | |||||||
\(152\) | 3.43804 | + | 5.95486i | 0.278862 | + | 0.483003i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.64157 | − | 0.148737i | −0.212864 | − | 0.0119856i | ||||
\(155\) | 9.49181i | 0.762401i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.80476 | + | 1.61933i | 0.223844 | + | 0.129236i | 0.607729 | − | 0.794145i | \(-0.292081\pi\) |
−0.383885 | + | 0.923381i | \(0.625414\pi\) | |||||||
\(158\) | 9.88689 | + | 5.70820i | 0.786559 | + | 0.454120i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 4.02536i | − | 0.318233i | ||||||
\(161\) | −5.68404 | + | 2.86839i | −0.447965 | + | 0.226061i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.34104 | − | 12.7151i | −0.574995 | − | 0.995920i | −0.996042 | − | 0.0888816i | \(-0.971671\pi\) |
0.421047 | − | 0.907039i | \(-0.361663\pi\) | |||||||
\(164\) | 2.63671 | − | 4.56691i | 0.205892 | − | 0.356616i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.4278 | + | 6.59784i | −0.886969 | + | 0.512092i | ||||
\(167\) | −15.0124 | −1.16169 | −0.580847 | − | 0.814013i | \(-0.697279\pi\) | ||||
−0.580847 | + | 0.814013i | \(0.697279\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −20.4571 | −1.57362 | ||||||||
\(170\) | 4.57148 | − | 2.63935i | 0.350617 | − | 0.202429i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.321005 | − | 0.555996i | 0.0244764 | − | 0.0423943i | ||||
\(173\) | 3.75098 | + | 6.49689i | 0.285182 | + | 0.493949i | 0.972653 | − | 0.232262i | \(-0.0746127\pi\) |
−0.687471 | + | 0.726211i | \(0.741279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.2406 | + | 24.7967i | −1.22767 | + | 1.87446i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.85081 | + | 1.06857i | 0.138724 | + | 0.0800924i | ||||
\(179\) | 4.78596 | + | 2.76318i | 0.357719 | + | 0.206529i | 0.668080 | − | 0.744090i | \(-0.267116\pi\) |
−0.310360 | + | 0.950619i | \(0.600450\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.64806i | − | 0.122499i | −0.998122 | − | 0.0612496i | \(-0.980491\pi\) | ||
0.998122 | − | 0.0612496i | \(-0.0195086\pi\) | |||||||
\(182\) | 6.89462 | + | 13.6625i | 0.511063 | + | 1.01273i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.20321 | − | 2.08402i | −0.0887018 | − | 0.153636i | ||||
\(185\) | 17.4636 | − | 30.2479i | 1.28395 | − | 2.22387i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13567 | − | 0.655680i | 0.0830484 | − | 0.0479480i | ||||
\(188\) | −11.9988 | −0.875104 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 27.6787 | 2.00802 | ||||||||
\(191\) | −7.25034 | + | 4.18599i | −0.524616 | + | 0.302887i | −0.738821 | − | 0.673901i | \(-0.764617\pi\) |
0.214205 | + | 0.976789i | \(0.431284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.381727 | − | 0.661170i | 0.0274773 | − | 0.0475921i | −0.851960 | − | 0.523607i | \(-0.824586\pi\) |
0.879437 | + | 0.476015i | \(0.157919\pi\) | |||||||
\(194\) | 7.69179 | + | 13.3226i | 0.552238 | + | 0.956505i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.15840 | − | 5.63096i | 0.297028 | − | 0.402212i | ||||
\(197\) | 9.08208i | 0.647072i | 0.946216 | + | 0.323536i | \(0.104872\pi\) | ||||
−0.946216 | + | 0.323536i | \(0.895128\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2515 | + | 7.07339i | 0.868484 | + | 0.501420i | 0.866844 | − | 0.498579i | \(-0.166145\pi\) |
0.00163989 | + | 0.999999i | \(0.499478\pi\) | |||||||
\(200\) | −9.70255 | − | 5.60177i | −0.686074 | − | 0.396105i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 16.1348i | − | 1.13524i | ||||||
\(203\) | −0.0789670 | + | 1.40245i | −0.00554239 | + | 0.0984328i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.6137 | − | 18.3835i | −0.741293 | − | 1.28396i | ||||
\(206\) | 2.46325 | − | 4.26648i | 0.171623 | − | 0.297259i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.00927 | + | 2.89210i | −0.347330 | + | 0.200531i | ||||
\(209\) | 6.87608 | 0.475628 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9602 | 1.71833 | 0.859166 | − | 0.511698i | \(-0.170983\pi\) | ||||
0.859166 | + | 0.511698i | \(0.170983\pi\) | |||||||
\(212\) | −2.35898 | + | 1.36196i | −0.162015 | + | 0.0935397i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.15605 | − | 5.46644i | 0.215743 | − | 0.373678i | ||||
\(215\) | −1.29216 | − | 2.23809i | −0.0881245 | − | 0.152636i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.21896 | − | 3.41814i | −0.354286 | − | 0.232039i | ||||
\(218\) | 18.4639i | 1.25054i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.48607 | − | 2.01268i | −0.235030 | − | 0.135695i | ||||
\(221\) | −6.56895 | − | 3.79259i | −0.441876 | − | 0.255117i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.46095i | − | 0.0978323i | −0.998803 | − | 0.0489161i | \(-0.984423\pi\) | ||
0.998803 | − | 0.0489161i | \(-0.0155767\pi\) | |||||||
\(224\) | 2.21330 | + | 1.44959i | 0.147882 | + | 0.0968550i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.23968 | + | 2.14719i | 0.0824624 | + | 0.142829i | ||||
\(227\) | 10.4814 | − | 18.1544i | 0.695678 | − | 1.20495i | −0.274274 | − | 0.961652i | \(-0.588437\pi\) |
0.969952 | − | 0.243298i | \(-0.0782292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.5684 | + | 13.6072i | −1.55745 | + | 0.899191i | −0.559945 | + | 0.828530i | \(0.689178\pi\) |
−0.997500 | + | 0.0706615i | \(0.977489\pi\) | |||||||
\(230\) | −9.68671 | −0.638723 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.530917 | −0.0348564 | ||||||||
\(233\) | 5.80159 | − | 3.34955i | 0.380074 | − | 0.219436i | −0.297776 | − | 0.954636i | \(-0.596245\pi\) |
0.677851 | + | 0.735200i | \(0.262912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.1498 | + | 41.8287i | −1.57536 | + | 2.72860i | ||||
\(236\) | −0.834008 | − | 1.44455i | −0.0542893 | − | 0.0940319i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.195048 | + | 3.46404i | −0.0126431 | + | 0.224541i | ||||
\(239\) | − | 13.7992i | − | 0.892595i | −0.894885 | − | 0.446298i | \(-0.852742\pi\) | ||
0.894885 | − | 0.446298i | \(-0.147258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.1448 | − | 8.74387i | −0.975564 | − | 0.563242i | −0.0746361 | − | 0.997211i | \(-0.523780\pi\) |
−0.900928 | + | 0.433969i | \(0.857113\pi\) | |||||||
\(242\) | −0.866025 | − | 0.500000i | −0.0556702 | − | 0.0321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15.3404i | 0.982066i | ||||||||
\(245\) | −11.2604 | − | 25.8298i | −0.719399 | − | 1.65020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.8863 | − | 34.4442i | −1.26534 | − | 2.19163i | ||||
\(248\) | 1.17900 | − | 2.04209i | 0.0748666 | − | 0.129673i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −21.6259 | + | 12.4857i | −1.36774 | + | 0.789667i | ||||
\(251\) | 10.3791 | 0.655123 | 0.327562 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327562 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.40642 | −0.151290 | ||||||||
\(254\) | 4.51052 | − | 2.60415i | 0.283015 | − | 0.163399i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.82901 | + | 15.2923i | 0.550738 | + | 0.953907i | 0.998221 | + | 0.0596145i | \(0.0189871\pi\) |
−0.447483 | + | 0.894292i | \(0.647680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.3425 | + | 20.4949i | 0.642653 | + | 1.27349i | ||||
\(260\) | 23.2835i | 1.44398i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.34102 | − | 5.39304i | −0.577090 | − | 0.333183i | ||||
\(263\) | −2.62678 | − | 1.51657i | −0.161974 | − | 0.0935157i | 0.416822 | − | 0.908988i | \(-0.363144\pi\) |
−0.578796 | + | 0.815472i | \(0.696477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.9647i | 0.673559i | ||||||||
\(266\) | −9.96752 | + | 15.2188i | −0.611148 | + | 0.933125i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.09028 | + | 5.35251i | 0.188769 | + | 0.326957i | ||||
\(269\) | 2.42629 | − | 4.20246i | 0.147934 | − | 0.256228i | −0.782530 | − | 0.622613i | \(-0.786071\pi\) |
0.930464 | + | 0.366384i | \(0.119404\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.56205 | − | 1.47920i | 0.155633 | − | 0.0898549i | −0.420161 | − | 0.907450i | \(-0.638026\pi\) |
0.575794 | + | 0.817595i | \(0.304693\pi\) | |||||||
\(272\) | −1.31136 | −0.0795128 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4799 | −0.753937 | ||||||||
\(275\) | −9.70255 | + | 5.60177i | −0.585086 | + | 0.337799i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.74172 | + | 9.94495i | −0.344987 | + | 0.597534i | −0.985351 | − | 0.170537i | \(-0.945450\pi\) |
0.640365 | + | 0.768071i | \(0.278783\pi\) | |||||||
\(278\) | −1.25923 | − | 2.18105i | −0.0755235 | − | 0.130811i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.50804 | − | 4.79812i | 0.568214 | − | 0.286743i | ||||
\(281\) | 11.1113i | 0.662847i | 0.943482 | + | 0.331424i | \(0.107529\pi\) | ||||
−0.943482 | + | 0.331424i | \(0.892471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.32185 | + | 1.34052i | 0.138019 | + | 0.0796856i | 0.567420 | − | 0.823429i | \(-0.307942\pi\) |
−0.429400 | + | 0.903114i | \(0.641275\pi\) | |||||||
\(284\) | −10.4383 | − | 6.02654i | −0.619398 | − | 0.357609i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.78421i | 0.342027i | ||||||||
\(287\) | 13.9301 | + | 0.784352i | 0.822266 | + | 0.0462988i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.64017 | + | 13.2332i | 0.449422 | + | 0.778421i | ||||
\(290\) | −1.06857 | + | 1.85081i | −0.0627483 | + | 0.108683i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.5428 | + | 6.08687i | −0.616969 | + | 0.356207i | ||||
\(293\) | −6.53620 | −0.381849 | −0.190924 | − | 0.981605i | \(-0.561149\pi\) | ||||
−0.190924 | + | 0.981605i | \(0.561149\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.71437 | −0.390926 | ||||||||
\(296\) | −7.51433 | + | 4.33840i | −0.436762 | + | 0.252164i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.90830 | + | 8.50142i | −0.284330 | + | 0.492474i | ||||
\(299\) | 6.95962 | + | 12.0544i | 0.402485 | + | 0.697124i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.69591 | + | 0.0954905i | 0.0977506 | + | 0.00550398i | ||||
\(302\) | − | 9.54881i | − | 0.549472i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.95486 | − | 3.43804i | −0.341535 | − | 0.197185i | ||||
\(305\) | 53.4775 | + | 30.8753i | 3.06211 | + | 1.76791i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.9592i | 1.93815i | 0.246760 | + | 0.969077i | \(0.420634\pi\) | ||||
−0.246760 | + | 0.969077i | \(0.579366\pi\) | |||||||
\(308\) | 2.36203 | − | 1.19197i | 0.134589 | − | 0.0679190i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.74591 | − | 8.22015i | −0.269549 | − | 0.466873i | ||||
\(311\) | −12.7067 | + | 22.0087i | −0.720533 | + | 1.24800i | 0.240253 | + | 0.970710i | \(0.422770\pi\) |
−0.960786 | + | 0.277290i | \(0.910564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.44097 | − | 4.29605i | 0.420589 | − | 0.242827i | −0.274740 | − | 0.961518i | \(-0.588592\pi\) |
0.695329 | + | 0.718691i | \(0.255259\pi\) | |||||||
\(314\) | −3.23865 | −0.182768 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.4164 | −0.642222 | ||||||||
\(317\) | −5.95841 | + | 3.44009i | −0.334658 | + | 0.193215i | −0.657907 | − | 0.753099i | \(-0.728558\pi\) |
0.323249 | + | 0.946314i | \(0.395225\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.265458 | + | 0.459787i | −0.0148628 | + | 0.0257431i | ||||
\(320\) | 2.01268 | + | 3.48607i | 0.112512 | + | 0.194877i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.48833 | − | 5.32612i | 0.194397 | − | 0.296813i | ||||
\(323\) | − | 9.01701i | − | 0.501720i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 56.1215 | + | 32.4018i | 3.11306 | + | 1.79733i | ||||
\(326\) | 12.7151 | + | 7.34104i | 0.704222 | + | 0.406583i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.27341i | 0.291176i | ||||||||
\(329\) | −14.3023 | − | 28.3416i | −0.788510 | − | 1.56252i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.58577 | + | 7.94279i | 0.252057 | + | 0.436575i | 0.964092 | − | 0.265569i | \(-0.0855597\pi\) |
−0.712035 | + | 0.702144i | \(0.752226\pi\) | |||||||
\(332\) | 6.59784 | − | 11.4278i | 0.362104 | − | 0.627182i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.0011 | − | 7.50620i | 0.711390 | − | 0.410721i | ||||
\(335\) | 24.8790 | 1.35928 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3285 | 0.671578 | 0.335789 | − | 0.941937i | \(-0.390997\pi\) | ||||
0.335789 | + | 0.941937i | \(0.390997\pi\) | |||||||
\(338\) | 17.7163 | − | 10.2285i | 0.963642 | − | 0.556359i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.63935 | + | 4.57148i | −0.143139 | + | 0.247923i | ||||
\(341\) | −1.17900 | − | 2.04209i | −0.0638465 | − | 0.110585i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2572 | + | 3.11032i | 0.985797 | + | 0.167941i | ||||
\(344\) | 0.642009i | 0.0346148i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.49689 | − | 3.75098i | −0.349275 | − | 0.201654i | ||||
\(347\) | −19.5559 | − | 11.2906i | −1.04982 | − | 0.606112i | −0.127219 | − | 0.991875i | \(-0.540605\pi\) |
−0.922598 | + | 0.385762i | \(0.873938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.3095i | − | 1.24773i | −0.781532 | − | 0.623866i | \(-0.785561\pi\) | ||
0.781532 | − | 0.623866i | \(-0.214439\pi\) | |||||||
\(350\) | 1.66638 | − | 29.5949i | 0.0890718 | − | 1.58191i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 8.16582 | − | 14.1436i | 0.434623 | − | 0.752789i | −0.562642 | − | 0.826701i | \(-0.690215\pi\) |
0.997265 | + | 0.0739120i | \(0.0235484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.0178 | + | 24.2590i | −2.23007 | + | 1.28753i | ||||
\(356\) | −2.13713 | −0.113268 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.52635 | −0.292077 | ||||||||
\(359\) | −14.8416 | + | 8.56882i | −0.783311 | + | 0.452245i | −0.837603 | − | 0.546280i | \(-0.816043\pi\) |
0.0542911 | + | 0.998525i | \(0.482710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.1402 | − | 24.4916i | 0.744224 | − | 1.28903i | ||||
\(362\) | 0.824029 | + | 1.42726i | 0.0433100 | + | 0.0750151i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.8022 | − | 8.38475i | −0.671016 | − | 0.439480i | ||||
\(365\) | 49.0037i | 2.56497i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.8720 | − | 10.3184i | −0.932911 | − | 0.538616i | −0.0451800 | − | 0.998979i | \(-0.514386\pi\) |
−0.887731 | + | 0.460362i | \(0.847719\pi\) | |||||||
\(368\) | 2.08402 | + | 1.20321i | 0.108637 | + | 0.0627216i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 34.9273i | 1.81578i | ||||||||
\(371\) | −6.02883 | − | 3.94857i | −0.313001 | − | 0.205000i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.52356 | + | 2.63889i | 0.0788871 | + | 0.136637i | 0.902770 | − | 0.430124i | \(-0.141530\pi\) |
−0.823883 | + | 0.566760i | \(0.808197\pi\) | |||||||
\(374\) | −0.655680 | + | 1.13567i | −0.0339044 | + | 0.0587241i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.3913 | − | 5.99941i | 0.535890 | − | 0.309396i | ||||
\(377\) | 3.07093 | 0.158161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.5315 | 1.41420 | 0.707100 | − | 0.707113i | \(-0.250003\pi\) | ||||
0.707100 | + | 0.707113i | \(0.250003\pi\) | |||||||
\(380\) | −23.9705 | + | 13.8394i | −1.22966 | + | 0.709944i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.18599 | − | 7.25034i | 0.214174 | − | 0.370960i | ||||
\(383\) | 7.25284 | + | 12.5623i | 0.370603 | + | 0.641903i | 0.989658 | − | 0.143444i | \(-0.0458177\pi\) |
−0.619055 | + | 0.785347i | \(0.712484\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.598720 | − | 10.6333i | 0.0305136 | − | 0.541921i | ||||
\(386\) | 0.763454i | 0.0388588i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.3226 | − | 7.69179i | −0.676351 | − | 0.390492i | ||||
\(389\) | 6.36070 | + | 3.67235i | 0.322501 | + | 0.186196i | 0.652507 | − | 0.757783i | \(-0.273717\pi\) |
−0.330006 | + | 0.943979i | \(0.607051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.15568i | 0.159590i | ||||||||
\(392\) | −0.785798 | + | 6.95575i | −0.0396888 | + | 0.351319i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.54104 | − | 7.86532i | −0.228774 | − | 0.396249i | ||||
\(395\) | −22.9776 | + | 39.7983i | −1.15613 | + | 2.00247i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.2219 | − | 11.0977i | 0.964717 | − | 0.556980i | 0.0670957 | − | 0.997747i | \(-0.478627\pi\) |
0.897622 | + | 0.440767i | \(0.145293\pi\) | |||||||
\(398\) | −14.1468 | −0.709114 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.2035 | 0.560177 | ||||||||
\(401\) | 6.13684 | − | 3.54311i | 0.306459 | − | 0.176934i | −0.338882 | − | 0.940829i | \(-0.610049\pi\) |
0.645341 | + | 0.763895i | \(0.276715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.81959 | + | 11.8119i | −0.339708 | + | 0.588391i | ||||
\(404\) | 8.06738 | + | 13.9731i | 0.401367 | + | 0.695188i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.632839 | − | 1.25404i | −0.0314073 | − | 0.0622371i | ||||
\(407\) | 8.67680i | 0.430093i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.2627 | + | 8.81191i | 0.754691 | + | 0.435721i | 0.827386 | − | 0.561633i | \(-0.189827\pi\) |
−0.0726956 | + | 0.997354i | \(0.523160\pi\) | |||||||
\(410\) | 18.3835 | + | 10.6137i | 0.907895 | + | 0.524173i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.92650i | 0.242711i | ||||||||
\(413\) | 2.41795 | − | 3.69181i | 0.118979 | − | 0.181662i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.5587 | − | 46.0010i | −1.30372 | − | 2.25810i | ||||
\(416\) | 2.89210 | − | 5.00927i | 0.141797 | − | 0.245600i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.95486 | + | 3.43804i | −0.291262 | + | 0.168160i | ||||
\(419\) | 33.7027 | 1.64649 | 0.823243 | − | 0.567689i | \(-0.192162\pi\) | ||||
0.823243 | + | 0.567689i | \(0.192162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.1841 | 1.81224 | 0.906120 | − | 0.423020i | \(-0.139030\pi\) | ||||
0.906120 | + | 0.423020i | \(0.139030\pi\) | |||||||
\(422\) | −21.6162 | + | 12.4801i | −1.05226 | + | 0.607522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.36196 | − | 2.35898i | 0.0661425 | − | 0.114562i | ||||
\(425\) | 7.34593 | + | 12.7235i | 0.356330 | + | 0.617181i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.2344 | + | 18.2853i | −1.75351 | + | 0.884888i | ||||
\(428\) | 6.31210i | 0.305107i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.23809 | + | 1.29216i | 0.107930 | + | 0.0623135i | ||||
\(431\) | 16.0885 | + | 9.28867i | 0.774953 | + | 0.447420i | 0.834639 | − | 0.550798i | \(-0.185676\pi\) |
−0.0596854 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.4162i | − | 1.55782i | −0.627135 | − | 0.778910i | \(-0.715773\pi\) | ||
0.627135 | − | 0.778910i | \(-0.284227\pi\) | |||||||
\(434\) | 6.22882 | + | 0.350722i | 0.298993 | + | 0.0168352i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.23197 | − | 15.9902i | −0.442131 | − | 0.765794i | ||||
\(437\) | −8.27337 | + | 14.3299i | −0.395769 | + | 0.685492i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.9271 | + | 8.04080i | −0.664703 | + | 0.383766i | −0.794067 | − | 0.607831i | \(-0.792040\pi\) |
0.129364 | + | 0.991597i | \(0.458707\pi\) | |||||||
\(440\) | 4.02536 | 0.191902 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.58517 | 0.360790 | ||||||||
\(443\) | 23.9276 | − | 13.8146i | 1.13683 | − | 0.656352i | 0.191190 | − | 0.981553i | \(-0.438765\pi\) |
0.945645 | + | 0.325202i | \(0.105432\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.30136 | + | 7.45018i | −0.203904 | + | 0.353172i | ||||
\(446\) | 0.730474 | + | 1.26522i | 0.0345889 | + | 0.0599098i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.64157 | − | 0.148737i | −0.124802 | − | 0.00702716i | ||||
\(449\) | 33.3354i | 1.57319i | 0.617467 | + | 0.786597i | \(0.288159\pi\) | ||||
−0.617467 | + | 0.786597i | \(0.711841\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.56691 | + | 2.63671i | 0.215047 | + | 0.124158i | ||||
\(452\) | −2.14719 | − | 1.23968i | −0.100995 | − | 0.0583097i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.9629i | 0.983837i | ||||||||
\(455\) | −54.9965 | + | 27.7534i | −2.57827 | + | 1.30110i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.22365 | − | 3.85147i | −0.104018 | − | 0.180164i | 0.809319 | − | 0.587370i | \(-0.199837\pi\) |
−0.913337 | + | 0.407206i | \(0.866503\pi\) | |||||||
\(458\) | 13.6072 | − | 23.5684i | 0.635824 | − | 1.10128i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.38894 | − | 4.84335i | 0.391136 | − | 0.225823i | ||||
\(461\) | 13.4101 | 0.624570 | 0.312285 | − | 0.949988i | \(-0.398906\pi\) | ||||
0.312285 | + | 0.949988i | \(0.398906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.13394 | 0.238594 | 0.119297 | − | 0.992859i | \(-0.461936\pi\) | ||||
0.119297 | + | 0.992859i | \(0.461936\pi\) | |||||||
\(464\) | 0.459787 | − | 0.265458i | 0.0213451 | − | 0.0123236i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.34955 | + | 5.80159i | −0.155165 | + | 0.268753i | ||||
\(467\) | −6.89106 | − | 11.9357i | −0.318880 | − | 0.552317i | 0.661374 | − | 0.750056i | \(-0.269973\pi\) |
−0.980255 | + | 0.197739i | \(0.936640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.95929 | + | 13.6794i | −0.413702 | + | 0.631656i | ||||
\(470\) | − | 48.2996i | − | 2.22789i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.44455 | + | 0.834008i | 0.0664906 | + | 0.0383884i | ||||
\(473\) | 0.555996 | + | 0.321005i | 0.0255647 | + | 0.0147598i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 77.0364i | 3.53467i | ||||||||
\(476\) | −1.56311 | − | 3.09747i | −0.0716448 | − | 0.141972i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.89959 | + | 11.9504i | 0.315580 | + | 0.546601i | ||||
\(479\) | 14.7319 | − | 25.5163i | 0.673116 | − | 1.16587i | −0.303900 | − | 0.952704i | \(-0.598289\pi\) |
0.977016 | − | 0.213167i | \(-0.0683778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 43.4645 | − | 25.0942i | 1.98181 | − | 1.14420i | ||||
\(482\) | 17.4877 | 0.796545 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −53.6282 | + | 30.9622i | −2.43513 | + | 1.40592i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0352 | − | 19.1135i | 0.500053 | − | 0.866117i | −0.499947 | − | 0.866056i | \(-0.666647\pi\) |
1.00000 | 6.08379e-5i | \(-1.93653e-5\pi\) | ||||||||
\(488\) | −7.67018 | − | 13.2851i | −0.347213 | − | 0.601390i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 22.6667 | + | 16.7391i | 1.02398 | + | 0.756193i | ||||
\(491\) | − | 18.0771i | − | 0.815810i | −0.913024 | − | 0.407905i | \(-0.866259\pi\) | ||
0.913024 | − | 0.407905i | \(-0.133741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.602946 | + | 0.348111i | 0.0271553 | + | 0.0156781i | ||||
\(494\) | 34.4442 | + | 19.8863i | 1.54972 | + | 0.894729i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.35800i | 0.105877i | ||||||||
\(497\) | 1.79274 | − | 31.8390i | 0.0804154 | − | 1.42818i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.368619 | − | 0.638467i | −0.0165017 | − | 0.0285817i | 0.857657 | − | 0.514223i | \(-0.171920\pi\) |
−0.874158 | + | 0.485641i | \(0.838586\pi\) | |||||||
\(500\) | 12.4857 | − | 21.6259i | 0.558379 | − | 0.967141i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.98857 | + | 5.18955i | −0.401180 | + | 0.231621i | ||||
\(503\) | −10.1774 | −0.453787 | −0.226894 | − | 0.973920i | \(-0.572857\pi\) | ||||
−0.226894 | + | 0.973920i | \(0.572857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.9483 | 2.89016 | ||||||||
\(506\) | 2.08402 | − | 1.20321i | 0.0926460 | − | 0.0534892i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.60415 | + | 4.51052i | −0.115540 | + | 0.200122i | ||||
\(509\) | −2.35282 | − | 4.07520i | −0.104287 | − | 0.180630i | 0.809160 | − | 0.587589i | \(-0.199923\pi\) |
−0.913447 | + | 0.406959i | \(0.866589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.9441 | − | 17.6470i | −1.19194 | − | 0.780656i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.2923 | − | 8.82901i | −0.674514 | − | 0.389431i | ||||
\(515\) | 17.1741 | + | 9.91548i | 0.756782 | + | 0.436928i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.9988i | − | 0.527708i | ||||||
\(518\) | −19.2043 | − | 12.5778i | −0.843790 | − | 0.552639i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11.6418 | − | 20.1641i | −0.510525 | − | 0.884256i | ||||
\(521\) | −3.19015 | + | 5.52550i | −0.139763 | + | 0.242077i | −0.927407 | − | 0.374054i | \(-0.877967\pi\) |
0.787644 | + | 0.616131i | \(0.211301\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.62477 | + | 2.09276i | −0.158500 | + | 0.0915101i | −0.577152 | − | 0.816637i | \(-0.695836\pi\) |
0.418652 | + | 0.908147i | \(0.362503\pi\) | |||||||
\(524\) | 10.7861 | 0.471192 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.03314 | 0.132251 | ||||||||
\(527\) | −2.67791 | + | 1.54609i | −0.116652 | + | 0.0673489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.60457 | + | 14.9036i | −0.374112 | + | 0.647981i | ||||
\(530\) | −5.48237 | − | 9.49575i | −0.238139 | − | 0.412469i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.02273 | − | 18.1636i | 0.0443409 | − | 0.787493i | ||||
\(533\) | − | 30.5025i | − | 1.32121i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.0044 | + | 12.7042i | 0.951333 | + | 0.549252i | ||||
\(536\) | −5.35251 | − | 3.09028i | −0.231193 | − | 0.133480i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.85258i | 0.209210i | ||||||||
\(539\) | 5.63096 | + | 4.15840i | 0.242543 | + | 0.179115i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.177282 | + | 0.307061i | 0.00762194 | + | 0.0132016i | 0.869811 | − | 0.493385i | \(-0.164241\pi\) |
−0.862189 | + | 0.506586i | \(0.830907\pi\) | |||||||
\(542\) | −1.47920 | + | 2.56205i | −0.0635370 | + | 0.110049i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.13567 | − | 0.655680i | 0.0486915 | − | 0.0281120i | ||||
\(545\) | −74.3240 | −3.18369 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.859833 | 0.0367638 | 0.0183819 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183819 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(548\) | 10.8079 | − | 6.23994i | 0.461690 | − | 0.266557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.60177 | − | 9.70255i | 0.238860 | − | 0.413718i | ||||
\(551\) | 1.82531 | + | 3.16154i | 0.0777610 | + | 0.134686i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6080 | − | 26.9659i | −0.578673 | − | 1.14671i | ||||
\(554\) | − | 11.4834i | − | 0.487885i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.18105 | + | 1.25923i | 0.0924971 | + | 0.0534032i | ||||
\(557\) | −24.4683 | − | 14.1268i | −1.03675 | − | 0.598570i | −0.117841 | − | 0.993032i | \(-0.537597\pi\) |
−0.918912 | + | 0.394463i | \(0.870931\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.71351i | − | 0.157065i | ||||||
\(560\) | −5.83514 | + | 8.90932i | −0.246580 | + | 0.376487i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.55567 | − | 9.62270i | −0.234352 | − | 0.405909i | ||||
\(563\) | 15.4121 | − | 26.6945i | 0.649542 | − | 1.12504i | −0.333691 | − | 0.942683i | \(-0.608294\pi\) |
0.983233 | − | 0.182356i | \(-0.0583725\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.64322 | + | 4.99017i | −0.363623 | + | 0.209938i | ||||
\(566\) | −2.68104 | −0.112692 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0531 | 0.505736 | ||||||||
\(569\) | 36.9884 | − | 21.3553i | 1.55063 | − | 0.895259i | 0.552544 | − | 0.833484i | \(-0.313657\pi\) |
0.998090 | − | 0.0617750i | \(-0.0196761\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6945 | + | 25.4516i | −0.614946 | + | 1.06512i | 0.375448 | + | 0.926844i | \(0.377489\pi\) |
−0.990394 | + | 0.138274i | \(0.955844\pi\) | |||||||
\(572\) | −2.89210 | − | 5.00927i | −0.120925 | − | 0.209448i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.4560 | + | 6.28577i | −0.519902 | + | 0.262363i | ||||
\(575\) | − | 26.9604i | − | 1.12433i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.27344 | − | 4.77667i | −0.344428 | − | 0.198855i | 0.317801 | − | 0.948158i | \(-0.397056\pi\) |
−0.662228 | + | 0.749302i | \(0.730389\pi\) | |||||||
\(578\) | −13.2332 | − | 7.64017i | −0.550427 | − | 0.317789i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.13713i | − | 0.0887396i | ||||||
\(581\) | 34.8573 | + | 1.96269i | 1.44612 | + | 0.0814260i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.36196 | − | 2.35898i | −0.0564066 | − | 0.0976990i | ||||
\(584\) | 6.08687 | − | 10.5428i | 0.251876 | − | 0.436263i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.66052 | − | 3.26810i | 0.233834 | − | 0.135004i | ||||
\(587\) | −23.4420 | −0.967554 | −0.483777 | − | 0.875191i | \(-0.660735\pi\) | ||||
−0.483777 | + | 0.875191i | \(0.660735\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.2138 | −0.668079 | ||||||||
\(590\) | 5.81482 | − | 3.35719i | 0.239392 | − | 0.138213i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.33840 | − | 7.51433i | 0.178307 | − | 0.308837i | ||||
\(593\) | 16.4622 | + | 28.5133i | 0.676020 | + | 1.17090i | 0.976170 | + | 0.217008i | \(0.0696299\pi\) |
−0.300150 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9440 | − | 0.785137i | −0.571649 | − | 0.0321875i | ||||
\(596\) | − | 9.81660i | − | 0.402103i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0544 | − | 6.95962i | −0.492941 | − | 0.284600i | ||||
\(599\) | −10.2217 | − | 5.90150i | −0.417647 | − | 0.241129i | 0.276423 | − | 0.961036i | \(-0.410851\pi\) |
−0.694070 | + | 0.719907i | \(0.744184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.5763i | − | 0.553787i | −0.960901 | − | 0.276894i | \(-0.910695\pi\) | ||
0.960901 | − | 0.276894i | \(-0.0893050\pi\) | |||||||
\(602\) | −1.51645 | + | 0.765258i | −0.0618057 | + | 0.0311896i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.77440 | + | 8.26951i | 0.194268 | + | 0.336482i | ||||
\(605\) | 2.01268 | − | 3.48607i | 0.0818271 | − | 0.141729i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.1502 | + | 11.0563i | −0.777281 | + | 0.448763i | −0.835466 | − | 0.549543i | \(-0.814802\pi\) |
0.0581850 | + | 0.998306i | \(0.481469\pi\) | |||||||
\(608\) | 6.87608 | 0.278862 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −61.7505 | −2.50021 | ||||||||
\(611\) | −60.1054 | + | 34.7018i | −2.43160 | + | 1.40389i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.34271 | + | 12.7179i | −0.296569 | + | 0.513673i | −0.975349 | − | 0.220669i | \(-0.929176\pi\) |
0.678780 | + | 0.734342i | \(0.262509\pi\) | |||||||
\(614\) | −16.9796 | − | 29.4095i | −0.685241 | − | 1.18687i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44959 | + | 2.21330i | −0.0584058 | + | 0.0891762i | ||||
\(617\) | − | 25.4764i | − | 1.02564i | −0.858496 | − | 0.512821i | \(-0.828601\pi\) | ||
0.858496 | − | 0.512821i | \(-0.171399\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6624 | − | 10.1974i | −0.709911 | − | 0.409868i | 0.101117 | − | 0.994875i | \(-0.467758\pi\) |
−0.811028 | + | 0.585007i | \(0.801092\pi\) | |||||||
\(620\) | 8.22015 | + | 4.74591i | 0.330129 | + | 0.190600i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 25.4135i | − | 1.01899i | ||||||
\(623\) | −2.54740 | − | 5.04797i | −0.102060 | − | 0.202243i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.2508 | − | 38.5394i | −0.890030 | − | 1.54158i | ||||
\(626\) | −4.29605 | + | 7.44097i | −0.171705 | + | 0.297401i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.80476 | − | 1.61933i | 0.111922 | − | 0.0646182i | ||||
\(629\) | 11.3784 | 0.453687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6750 | 1.22115 | 0.610576 | − | 0.791957i | \(-0.290938\pi\) | ||||
0.610576 | + | 0.791957i | \(0.290938\pi\) | |||||||
\(632\) | 9.88689 | − | 5.70820i | 0.393279 | − | 0.227060i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.44009 | − | 5.95841i | 0.136623 | − | 0.236639i | ||||
\(635\) | 10.4826 | + | 18.1565i | 0.415991 | + | 0.720517i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.54522 | − | 40.2335i | 0.180088 | − | 1.59411i | ||||
\(638\) | − | 0.530917i | − | 0.0210192i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.48607 | − | 2.01268i | −0.137799 | − | 0.0795582i | ||||
\(641\) | 19.4844 | + | 11.2493i | 0.769588 | + | 0.444322i | 0.832728 | − | 0.553683i | \(-0.186778\pi\) |
−0.0631395 | + | 0.998005i | \(0.520111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 35.8596i | − | 1.41417i | −0.707131 | − | 0.707083i | \(-0.750011\pi\) | ||
0.707131 | − | 0.707083i | \(-0.249989\pi\) | |||||||
\(644\) | −0.357924 | + | 6.35672i | −0.0141042 | + | 0.250490i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.50851 | + | 7.80896i | 0.177385 | + | 0.307239i | ||||
\(647\) | 14.2048 | − | 24.6034i | 0.558448 | − | 0.967261i | −0.439178 | − | 0.898400i | \(-0.644730\pi\) |
0.997626 | − | 0.0688607i | \(-0.0219364\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.44455 | − | 0.834008i | 0.0567034 | − | 0.0327377i | ||||
\(650\) | −64.8036 | −2.54181 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.6821 | −0.574995 | ||||||||
\(653\) | 21.5088 | − | 12.4181i | 0.841703 | − | 0.485958i | −0.0161395 | − | 0.999870i | \(-0.505138\pi\) |
0.857843 | + | 0.513912i | \(0.171804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.7089 | − | 37.6010i | 0.848238 | − | 1.46919i | ||||
\(656\) | −2.63671 | − | 4.56691i | −0.102946 | − | 0.178308i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26.5569 | + | 17.3934i | 1.03530 | + | 0.678066i | ||||
\(659\) | 16.6910i | 0.650190i | 0.945681 | + | 0.325095i | \(0.105396\pi\) | ||||
−0.945681 | + | 0.325095i | \(0.894604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.7814 | + | 15.4622i | 1.04167 | + | 0.601411i | 0.920307 | − | 0.391197i | \(-0.127939\pi\) |
0.121367 | + | 0.992608i | \(0.461272\pi\) | |||||||
\(662\) | −7.94279 | − | 4.58577i | −0.308705 | − | 0.178231i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.1957i | 0.512092i | ||||||||
\(665\) | −61.2612 | − | 40.1229i | −2.37561 | − | 1.55590i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.638804 | − | 1.10644i | −0.0247346 | − | 0.0428416i | ||||
\(668\) | −7.50620 | + | 13.0011i | −0.290424 | + | 0.503028i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.5458 | + | 12.4395i | −0.832387 | + | 0.480579i | ||||
\(671\) | −15.3404 | −0.592208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.4673 | −1.09733 | −0.548667 | − | 0.836041i | \(-0.684865\pi\) | ||||
−0.548667 | + | 0.836041i | \(0.684865\pi\) | |||||||
\(674\) | −10.6768 | + | 6.16427i | −0.411256 | + | 0.237439i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.2285 | + | 17.7163i | −0.393405 | + | 0.681398i | ||||
\(677\) | 10.4406 | + | 18.0836i | 0.401264 | + | 0.695010i | 0.993879 | − | 0.110476i | \(-0.0352377\pi\) |
−0.592615 | + | 0.805486i | \(0.701904\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28811 | − | 40.6368i | 0.0878095 | − | 1.55950i | ||||
\(680\) | − | 5.27869i | − | 0.202429i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.04209 | + | 1.17900i | 0.0781957 | + | 0.0451463i | ||||
\(683\) | −25.2149 | − | 14.5578i | −0.964822 | − | 0.557040i | −0.0671682 | − | 0.997742i | \(-0.521396\pi\) |
−0.897654 | + | 0.440701i | \(0.854730\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 50.2360i | − | 1.91942i | ||||||
\(686\) | −17.3664 | + | 6.43500i | −0.663051 | + | 0.245689i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.321005 | − | 0.555996i | −0.0122382 | − | 0.0211972i | ||||
\(689\) | −7.87785 | + | 13.6448i | −0.300122 | + | 0.519827i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.472662 | − | 0.272891i | 0.0179809 | − | 0.0103813i | −0.490983 | − | 0.871169i | \(-0.663362\pi\) |
0.508964 | + | 0.860788i | \(0.330029\pi\) | |||||||
\(692\) | 7.50196 | 0.285182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.5812 | 0.857172 | ||||||||
\(695\) | 8.77951 | − | 5.06885i | 0.333026 | − | 0.192272i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.45767 | − | 5.98886i | 0.130969 | − | 0.226844i | ||||
\(698\) | 11.6548 | + | 20.1867i | 0.441140 | + | 0.764076i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 13.3543 | + | 26.4631i | 0.504746 | + | 1.00021i | ||||
\(701\) | − | 18.0854i | − | 0.683076i | −0.939868 | − | 0.341538i | \(-0.889052\pi\) | ||
0.939868 | − | 0.341538i | \(-0.110948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.6692 | + | 29.8312i | 1.94874 | + | 1.12511i | ||||
\(704\) | −0.866025 | − | 0.500000i | −0.0326396 | − | 0.0188445i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.3316i | 0.614649i | ||||||||
\(707\) | −23.3889 | + | 35.7110i | −0.879628 | + | 1.34305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.5429 | + | 21.7249i | 0.471058 | + | 0.815897i | 0.999452 | − | 0.0331026i | \(-0.0105388\pi\) |
−0.528394 | + | 0.848999i | \(0.677205\pi\) | |||||||
\(710\) | 24.2590 | − | 42.0178i | 0.910424 | − | 1.57690i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.85081 | − | 1.06857i | 0.0693620 | − | 0.0400462i | ||||
\(713\) | 5.67434 | 0.212506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.2835 | −0.870755 | ||||||||
\(716\) | 4.78596 | − | 2.76318i | 0.178860 | − | 0.103265i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.56882 | − | 14.8416i | 0.319786 | − | 0.553885i | ||||
\(719\) | −4.50368 | − | 7.80060i | −0.167959 | − | 0.290913i | 0.769743 | − | 0.638354i | \(-0.220384\pi\) |
−0.937702 | + | 0.347440i | \(0.887051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6366 | + | 5.87226i | −0.433368 | + | 0.218694i | ||||
\(722\) | 28.2805i | 1.05249i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.42726 | − | 0.824029i | −0.0530437 | − | 0.0306248i | ||||
\(725\) | −5.15124 | − | 2.97407i | −0.191312 | − | 0.110454i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.52605i | − | 0.167862i | −0.996472 | − | 0.0839309i | \(-0.973253\pi\) | ||
0.996472 | − | 0.0839309i | \(-0.0267475\pi\) | |||||||
\(728\) | 15.2794 | + | 0.860326i | 0.566291 | + | 0.0318858i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.5018 | − | 42.4384i | −0.906854 | − | 1.57072i | ||||
\(731\) | 0.420952 | − | 0.729111i | 0.0155695 | − | 0.0269671i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.2535 | − | 12.2707i | 0.785016 | − | 0.453229i | −0.0531893 | − | 0.998584i | \(-0.516939\pi\) |
0.838205 | + | 0.545355i | \(0.183605\pi\) | |||||||
\(734\) | 20.6368 | 0.761719 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.40642 | −0.0887018 | ||||||||
\(737\) | −5.35251 | + | 3.09028i | −0.197162 | + | 0.113832i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.893650 | − | 1.54785i | 0.0328735 | − | 0.0569385i | −0.849121 | − | 0.528199i | \(-0.822867\pi\) |
0.881994 | + | 0.471261i | \(0.156201\pi\) | |||||||
\(740\) | −17.4636 | − | 30.2479i | −0.641976 | − | 1.11194i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.19541 | + | 0.405147i | 0.264152 | + | 0.0148734i | ||||
\(743\) | 18.8397i | 0.691162i | 0.938389 | + | 0.345581i | \(0.112318\pi\) | ||||
−0.938389 | + | 0.345581i | \(0.887682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.2213 | − | 19.7577i | −1.25377 | − | 0.723865i | ||||
\(746\) | −2.63889 | − | 1.52356i | −0.0966166 | − | 0.0557816i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.31136i | − | 0.0479480i | ||||||
\(749\) | −14.9094 | + | 7.52386i | −0.544777 | + | 0.274916i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.2768 | + | 22.9961i | 0.484478 | + | 0.839141i | 0.999841 | − | 0.0178314i | \(-0.00567621\pi\) |
−0.515363 | + | 0.856972i | \(0.672343\pi\) | |||||||
\(752\) | −5.99941 | + | 10.3913i | −0.218776 | + | 0.378931i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.65951 | + | 1.53547i | −0.0968535 | + | 0.0559184i | ||||
\(755\) | 38.4374 | 1.39888 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.49203 | −0.308648 | −0.154324 | − | 0.988020i | \(-0.549320\pi\) | ||||
−0.154324 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(758\) | −23.8430 | + | 13.7658i | −0.866017 | + | 0.499995i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.8394 | − | 23.9705i | 0.502006 | − | 0.869500i | ||||
\(761\) | 21.5357 | + | 37.3010i | 0.780670 | + | 1.35216i | 0.931552 | + | 0.363608i | \(0.118455\pi\) |
−0.150882 | + | 0.988552i | \(0.548211\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.7652 | − | 40.8662i | 0.968966 | − | 1.47945i | ||||
\(764\) | 8.37197i | 0.302887i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.5623 | − | 7.25284i | −0.453894 | − | 0.262056i | ||||
\(767\) | −8.35555 | − | 4.82408i | −0.301701 | − | 0.174187i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9802i | 0.540198i | 0.962833 | + | 0.270099i | \(0.0870565\pi\) | ||||
−0.962833 | + | 0.270099i | \(0.912944\pi\) | |||||||
\(770\) | 4.79812 | + | 9.50804i | 0.172912 | + | 0.342646i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.381727 | − | 0.661170i | −0.0137387 | − | 0.0237960i | ||||
\(773\) | 21.0099 | − | 36.3902i | 0.755673 | − | 1.30886i | −0.189366 | − | 0.981907i | \(-0.560643\pi\) |
0.945039 | − | 0.326958i | \(-0.106023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.8786 | − | 13.2090i | 0.821824 | − | 0.474481i | ||||
\(776\) | 15.3836 | 0.552238 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.34471 | −0.263321 | ||||||||
\(779\) | 31.4024 | − | 18.1302i | 1.12511 | − | 0.649582i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.02654 | − | 10.4383i | 0.215647 | − | 0.373511i | ||||
\(782\) | −1.57784 | − | 2.73290i | −0.0564234 | − | 0.0977283i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.79736 | − | 6.41676i | −0.0999056 | − | 0.229170i | ||||
\(785\) | − | 13.0368i | − | 0.465302i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.31665 | + | 3.06957i | 0.189518 | + | 0.109418i | 0.591757 | − | 0.806116i | \(-0.298435\pi\) |
−0.402239 | + | 0.915535i | \(0.631768\pi\) | |||||||
\(788\) | 7.86532 | + | 4.54104i | 0.280190 | + | 0.161768i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 45.9551i | − | 1.63501i | ||||||
\(791\) | 0.368773 | − | 6.54940i | 0.0131121 | − | 0.232870i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.3659 | + | 76.8441i | 1.57548 | + | 2.72881i | ||||
\(794\) | −11.0977 | + | 19.2219i | −0.393844 | + | 0.682158i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.2515 | − | 7.07339i | 0.434242 | − | 0.250710i | ||||
\(797\) | −25.7793 | −0.913149 | −0.456575 | − | 0.889685i | \(-0.650924\pi\) | ||||
−0.456575 | + | 0.889685i | \(0.650924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.7348 | −0.556656 | ||||||||
\(800\) | −9.70255 | + | 5.60177i | −0.343037 | + | 0.198052i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.54311 | + | 6.13684i | −0.125111 | + | 0.216699i | ||||
\(803\) | −6.08687 | − | 10.5428i | −0.214801 | − | 0.372046i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.4396 | + | 14.0418i | 0.755645 | + | 0.494908i | ||||
\(806\) | − | 13.6392i | − | 0.480419i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.9731 | − | 8.06738i | −0.491572 | − | 0.283810i | ||||
\(809\) | −48.4673 | − | 27.9826i | −1.70402 | − | 0.983816i | −0.941601 | − | 0.336731i | \(-0.890679\pi\) |
−0.762418 | − | 0.647085i | \(-0.775988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43.6485i | 1.53271i | 0.642420 | + | 0.766353i | \(0.277930\pi\) | ||||
−0.642420 | + | 0.766353i | \(0.722070\pi\) | |||||||
\(812\) | 1.17508 | + | 0.769613i | 0.0412371 | + | 0.0270081i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.33840 | − | 7.51433i | −0.152061 | − | 0.263377i | ||||
\(815\) | −29.5503 | + | 51.1827i | −1.03510 | + | 1.79285i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.82307 | − | 2.20725i | 0.133752 | − | 0.0772220i | ||||
\(818\) | −17.6238 | −0.616202 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.2274 | −0.741293 | ||||||||
\(821\) | 33.4917 | − | 19.3364i | 1.16887 | − | 0.674845i | 0.215454 | − | 0.976514i | \(-0.430877\pi\) |
0.953413 | + | 0.301669i | \(0.0975436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.08198 | + | 1.87405i | −0.0377156 | + | 0.0653253i | −0.884267 | − | 0.466982i | \(-0.845341\pi\) |
0.846551 | + | 0.532307i | \(0.178675\pi\) | |||||||
\(824\) | −2.46325 | − | 4.26648i | −0.0858114 | − | 0.148630i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.248096 | + | 4.40618i | −0.00863236 | + | 0.153311i | ||||
\(827\) | − | 19.9185i | − | 0.692633i | −0.938118 | − | 0.346317i | \(-0.887432\pi\) | ||
0.938118 | − | 0.346317i | \(-0.112568\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.2441 | + | 20.9255i | 1.25881 | + | 0.726773i | 0.972843 | − | 0.231467i | \(-0.0743524\pi\) |
0.285965 | + | 0.958240i | \(0.407686\pi\) | |||||||
\(830\) | 46.0010 | + | 26.5587i | 1.59672 | + | 0.921866i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.78421i | 0.200531i | ||||||||
\(833\) | 5.45315 | − | 7.38421i | 0.188941 | − | 0.255848i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.2152 | + | 52.3342i | 1.04564 | + | 1.81110i | ||||
\(836\) | 3.43804 | − | 5.95486i | 0.118907 | − | 0.205953i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29.1874 | + | 16.8514i | −1.00826 | + | 0.582121i | ||||
\(839\) | 39.5351 | 1.36490 | 0.682452 | − | 0.730931i | \(-0.260914\pi\) | ||||
0.682452 | + | 0.730931i | \(0.260914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7181 | 0.990280 | ||||||||
\(842\) | −32.2023 | + | 18.5920i | −1.10977 | + | 0.640724i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.4801 | − | 21.6162i | 0.429583 | − | 0.744059i | ||||
\(845\) | 41.1735 | + | 71.3147i | 1.41641 | + | 2.45330i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.19197 | + | 2.36203i | 0.0409567 | + | 0.0811604i | ||||
\(848\) | 2.72392i | 0.0935397i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.7235 | − | 7.34593i | −0.436413 | − | 0.251963i | ||||
\(851\) | −18.0826 | − | 10.4400i | −0.619865 | − | 0.357879i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17.9975i | − | 0.616221i | −0.951351 | − | 0.308111i | \(-0.900303\pi\) | ||
0.951351 | − | 0.308111i | \(-0.0996967\pi\) | |||||||
\(854\) | 22.2373 | − | 33.9528i | 0.760945 | − | 1.16184i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.15605 | − | 5.46644i | −0.107872 | − | 0.186839i | ||||
\(857\) | −2.78701 | + | 4.82725i | −0.0952026 | + | 0.164896i | −0.909693 | − | 0.415281i | \(-0.863683\pi\) |
0.814491 | + | 0.580177i | \(0.197017\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.7836 | − | 22.3917i | 1.32328 | − | 0.763996i | 0.339030 | − | 0.940776i | \(-0.389901\pi\) |
0.984251 | + | 0.176779i | \(0.0565679\pi\) | |||||||
\(860\) | −2.58432 | −0.0881245 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18.5773 | −0.632747 | ||||||||
\(863\) | −28.4143 | + | 16.4050i | −0.967233 | + | 0.558432i | −0.898392 | − | 0.439195i | \(-0.855264\pi\) |
−0.0688414 | + | 0.997628i | \(0.521930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0991 | − | 26.1523i | 0.513383 | − | 0.889206i | ||||
\(866\) | 16.2081 | + | 28.0732i | 0.550773 | + | 0.953967i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.56968 | + | 2.81068i | −0.189047 | + | 0.0954006i | ||||
\(869\) | − | 11.4164i | − | 0.387275i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.9601 | + | 17.8748i | 1.04904 | + | 0.605664i | ||||
\(872\) | 15.9902 | + | 9.23197i | 0.541498 | + | 0.312634i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 16.5467i | − | 0.559702i | ||||||
\(875\) | 65.9638 | + | 3.71418i | 2.22998 | + | 0.125562i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.4322 | − | 19.8012i | −0.386039 | − | 0.668640i | 0.605873 | − | 0.795561i | \(-0.292824\pi\) |
−0.991913 | + | 0.126921i | \(0.959490\pi\) | |||||||
\(878\) | 8.04080 | − | 13.9271i | 0.271364 | − | 0.470016i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.48607 | + | 2.01268i | −0.117515 | + | 0.0678475i | ||||
\(881\) | 38.3927 | 1.29348 | 0.646741 | − | 0.762709i | \(-0.276131\pi\) | ||||
0.646741 | + | 0.762709i | \(0.276131\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.23037 | 0.310627 | 0.155313 | − | 0.987865i | \(-0.450361\pi\) | ||||
0.155313 | + | 0.987865i | \(0.450361\pi\) | |||||||
\(884\) | −6.56895 | + | 3.79259i | −0.220938 | + | 0.127559i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.8146 | + | 23.9276i | −0.464111 | + | 0.803863i | ||||
\(887\) | 15.6602 | + | 27.1243i | 0.525819 | + | 0.910744i | 0.999548 | + | 0.0300738i | \(0.00957423\pi\) |
−0.473729 | + | 0.880671i | \(0.657092\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.7581 | − | 0.774666i | −0.461431 | − | 0.0259815i | ||||
\(890\) | − | 8.60273i | − | 0.288364i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.26522 | − | 0.730474i | −0.0423626 | − | 0.0244581i | ||||
\(893\) | −71.4513 | − | 41.2524i | −2.39103 | − | 1.38046i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 22.2456i | − | 0.743587i | ||||||
\(896\) | 2.36203 | − | 1.19197i | 0.0789100 | − | 0.0398210i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.6677 | − | 28.8693i | −0.556208 | − | 0.963381i | ||||
\(899\) | 0.625951 | − | 1.08418i | 0.0208766 | − | 0.0361594i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.09347 | + | 1.78602i | −0.103058 | + | 0.0595008i | ||||
\(902\) | −5.27341 | −0.175585 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.47936 | 0.0824624 | ||||||||
\(905\) | −5.74524 | + | 3.31701i | −0.190978 | + | 0.110261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.99860 | − | 17.3181i | 0.331998 | − | 0.575037i | −0.650905 | − | 0.759159i | \(-0.725611\pi\) |
0.982904 | + | 0.184121i | \(0.0589439\pi\) | |||||||
\(908\) | −10.4814 | − | 18.1544i | −0.347839 | − | 0.602475i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 33.7517 | − | 51.5333i | 1.11886 | − | 1.70831i | ||||
\(911\) | − | 19.9413i | − | 0.660683i | −0.943861 | − | 0.330342i | \(-0.892836\pi\) | ||
0.943861 | − | 0.330342i | \(-0.107164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.4278 | + | 6.59784i | 0.378205 | + | 0.218357i | ||||
\(914\) | 3.85147 | + | 2.22365i | 0.127395 | + | 0.0735517i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.2145i | 0.899191i | ||||||||
\(917\) | 12.8567 | + | 25.4771i | 0.424566 | + | 0.841327i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.2142 | − | 19.4235i | −0.369922 | − | 0.640723i | 0.619631 | − | 0.784893i | \(-0.287282\pi\) |
−0.989553 | + | 0.144170i | \(0.953949\pi\) | |||||||
\(920\) | −4.84335 | + | 8.38894i | −0.159681 | + | 0.276575i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.6135 | + | 6.70505i | −0.382470 | + | 0.220819i | ||||
\(923\) | −69.7175 | −2.29478 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −97.2109 | −3.19627 | ||||||||
\(926\) | −4.44612 | + | 2.56697i | −0.146109 | + | 0.0843559i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.265458 | + | 0.459787i | −0.00871410 | + | 0.0150933i | ||||
\(929\) | 11.5137 | + | 19.9423i | 0.377752 | + | 0.654285i | 0.990735 | − | 0.135811i | \(-0.0433639\pi\) |
−0.612983 | + | 0.790096i | \(0.710031\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.1222 | − | 19.2349i | 1.44605 | − | 0.630397i | ||||
\(932\) | − | 6.69909i | − | 0.219436i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.9357 | + | 6.89106i | 0.390547 | + | 0.225482i | ||||
\(935\) | −4.57148 | − | 2.63935i | −0.149503 | − | 0.0863159i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.34940i | 0.240095i | 0.992768 | + | 0.120047i | \(0.0383046\pi\) | ||||
−0.992768 | + | 0.120047i | \(0.961695\pi\) | |||||||
\(938\) | 0.919277 | − | 16.3263i | 0.0300155 | − | 0.533074i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24.1498 | + | 41.8287i | 0.787680 | + | 1.36430i | ||||
\(941\) | 25.8829 | − | 44.8305i | 0.843758 | − | 1.46143i | −0.0429374 | − | 0.999078i | \(-0.513672\pi\) |
0.886695 | − | 0.462354i | \(-0.152995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9899 | + | 6.34502i | −0.357880 | + | 0.206622i | ||||
\(944\) | −1.66802 | −0.0542893 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.642009 | −0.0208735 | ||||||||
\(947\) | −40.8148 | + | 23.5644i | −1.32630 | + | 0.765741i | −0.984726 | − | 0.174113i | \(-0.944294\pi\) |
−0.341577 | + | 0.939854i | \(0.610961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.2077 | + | 60.9816i | −1.14289 | + | 1.97955i | ||||
\(950\) | −38.5182 | − | 66.7155i | −1.24970 | − | 2.16454i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.90243 | + | 1.90094i | 0.0940681 | + | 0.0616097i | ||||
\(953\) | 37.8914i | 1.22742i | 0.789530 | + | 0.613712i | \(0.210324\pi\) | ||||
−0.789530 | + | 0.613712i | \(0.789676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.1852 | + | 16.8501i | 0.944412 | + | 0.545257i | ||||
\(956\) | −11.9504 | − | 6.89959i | −0.386505 | − | 0.223149i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29.4637i | 0.951930i | ||||||||
\(959\) | 27.6217 | + | 18.0907i | 0.891950 | + | 0.584181i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7199 | − | 22.0315i | −0.410320 | − | 0.710695i | ||||
\(962\) | −25.0942 | + | 43.4645i | −0.809070 | + | 1.40135i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.1448 | + | 8.74387i | −0.487782 | + | 0.281621i | ||||
\(965\) | −3.07318 | −0.0989291 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4529 | −0.657722 | −0.328861 | − | 0.944378i | \(-0.606665\pi\) | ||||
−0.328861 | + | 0.944378i | \(0.606665\pi\) | |||||||
\(968\) | −0.866025 | + | 0.500000i | −0.0278351 | + | 0.0160706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.9622 | − | 53.6282i | 0.994138 | − | 1.72190i | ||||
\(971\) | −10.3951 | − | 18.0049i | −0.333596 | − | 0.577804i | 0.649619 | − | 0.760260i | \(-0.274929\pi\) |
−0.983214 | + | 0.182456i | \(0.941595\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.374588 | + | 6.65268i | −0.0120087 | + | 0.213275i | ||||
\(974\) | 22.0704i | 0.707181i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2851 | + | 7.67018i | 0.425247 | + | 0.245517i | ||||
\(977\) | −44.7812 | − | 25.8544i | −1.43268 | − | 0.827156i | −0.435352 | − | 0.900260i | \(-0.643376\pi\) |
−0.997324 | + | 0.0731040i | \(0.976709\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.13713i | − | 0.0683030i | ||||||
\(980\) | −27.9994 | − | 3.16312i | −0.894409 | − | 0.101042i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.03857 | + | 15.6553i | 0.288432 | + | 0.499580i | ||||
\(983\) | −10.5074 | + | 18.1994i | −0.335135 | + | 0.580470i | −0.983511 | − | 0.180850i | \(-0.942115\pi\) |
0.648376 | + | 0.761320i | \(0.275449\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.6607 | − | 18.2793i | 1.00879 | − | 0.582428i | ||||
\(986\) | −0.696222 | −0.0221722 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −39.7727 | −1.26534 | ||||||||
\(989\) | −1.33796 | + | 0.772472i | −0.0425447 | + | 0.0245632i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.56437 | + | 11.3698i | −0.208524 | + | 0.361174i | −0.951250 | − | 0.308421i | \(-0.900199\pi\) |
0.742726 | + | 0.669596i | \(0.233533\pi\) | |||||||
\(992\) | −1.17900 | − | 2.04209i | −0.0374333 | − | 0.0648364i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.3670 | + | 28.4698i | 0.455692 | + | 0.903006i | ||||
\(995\) | − | 56.9459i | − | 1.80531i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.72079 | + | 2.72555i | 0.149509 | + | 0.0863190i | 0.572888 | − | 0.819633i | \(-0.305823\pi\) |
−0.423379 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(998\) | 0.638467 | + | 0.368619i | 0.0202103 | + | 0.0116684i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.r.d.1277.6 | yes | 24 | |
3.2 | odd | 2 | inner | 1386.2.r.d.1277.7 | yes | 24 | |
7.5 | odd | 6 | inner | 1386.2.r.d.89.7 | yes | 24 | |
21.5 | even | 6 | inner | 1386.2.r.d.89.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.r.d.89.6 | ✓ | 24 | 21.5 | even | 6 | inner | |
1386.2.r.d.89.7 | yes | 24 | 7.5 | odd | 6 | inner | |
1386.2.r.d.1277.6 | yes | 24 | 1.1 | even | 1 | trivial | |
1386.2.r.d.1277.7 | yes | 24 | 3.2 | odd | 2 | inner |